Guest Author: Dr. Michael Wu
Lithium Technologies Inc.

Last time we had a little detour from SNA due to my participation at the Social CRM Panel at the Social Media Club. Before that, I’ve shown you some real social graphs from our client base (anonymous for obvious reason). We’ve seen the stereotypic conversation graph from Q&A communities as well as discussion communities. But most communities have both Q&A and discussion activities, so their conversation graph has characteristics from both types of social graphs.

So far, the only social graph metrics that we’ve look at are degree centrality (number of connections) and the PageRank score (authority). But I have computed 10 social graph metrics for each user, so I will show you what insights we can get from the less common graph metrics. I will use couple of anonymous examples from our client base again, so these social graphs are based on actual data. Okay, let’s get into it!

Who are the cliquish users?

Figure 1 is the social graph of a hi-tech hardware/software community that has both marketing and support functions. The data I used to build this conversation graph was collected over a 60-day window, and it has 1571 interacting users within this period. The social graph of this community is similar in some way to those we saw last week. It has similar fan-liked structures — which are the hallmark of a Q&A community — but there is also a densely interconnected cluster of users that mimic a discussion community.

What is different in this social graph is that I’ve remapped the clustering coefficient, which measures cliquishness (i.e. how selective or exclusive a user is) to color, but the dot size still represents degree centrality. I also play with the edge color and the background, but that is just for aesthetics. Few observations about this conversation social graph:

1. Neither the biggest dots nor the smallest dots are yellow
2. The yellow dots tend to have intermediate-to-small size
3. Most of the yellow dots are concentrated in the dense cluster
4. The experts (those surrounded by those fan-like structures) are usually red

What does this mean? It means:

1. Neither the most well connected user nor the least connected users are the most cliquish. The least connected users are the least connected for a reason. They are probably not talkative in the community to begin with. So obviously they are not going to form a clique with others. In contrary, the most connected users probably talk to many other users, so that the group is too large to form a tight clique where everyone talks to everyone else.
2. Cliquish users tend to have only a few connections, but not less than three. This is the manifestation of a well-known phenomenon in communications, where the communication efficiency within a group drops as the group grows larger. It is progressively harder for everyone to know all the members and talk to everyone else in larger groups.
3. Cliquish people like discussion. Discussions usually take place within a small group of users, where everyone in the group talks to everyone else about their opinions. In fact that is what a quintessential discussion group is. So people in the discussion groups tend to form a clique, and hence they show up yellowish in this social graph.
4. Experts are not selective about who they talk to. They will help any user equally; it is the topic that is important to them. Consequently, experts usually end up answering questions from many inquirers who don’t know each other, so they can’t possibly form a clique.

The Power of a Connector

Figure 2 is a very interesting social graph. It is a conversation graph of an enthusiast community in the entertainment industry. But it is fragmented and has four sub-communities. The data I used to construct this graph was collected from a 90-day window, and there are 1638 interacting users within this period.

Here, I’ve remapped the betweenness centrality (which measures how critical a user is for information diffusion) to dot size; and I’ve left the dot color to represent the PageRank score.

We can clearly see one huge red dot in the middle. This user is the most critical user for information diffusion in this community because he has the highest betweenness centrality (he is the biggest dot). However, he is not an authority figure; because he has low PageRank score (he is red). If you examine the graph carefully, you can see that he is not even very well connected. He only has 10 connections, which is a very low degree centrality compare to the yellow dots in this community.

So how can such poorly-connected user (low degree centrality) with little authority (low PageRank score) be so important for information diffusion? It has to do with where he resides in the social graph. He is what I would call a connector, because he sits at the junction between all the sub-communities and connects them. Without this connector, information diffusion across the sub-communities would be very inefficient. So this connector plays a crucial role in this community. Yet, if you try to find him using more conventional metrics, such as degree centrality (number of connection), reputation, authority, etc., you will surely miss him. Therefore some people also called them the hidden influencers.

Research by Wharton Marketing professors, Raghuram Iyengar and Christophe Van den Bulte, has validated the importance of such connector for word-of-mouth (WOM) information diffusion. This research was published at Knowledge @Wharton under the titled “The Buzz Starts Here: Finding the First Mouth for Word-of-Mouth Marketing.” I strongly recommend that you check it out (registration is free). If you don’t have time to read it, there is even a podcast that you can listen to or download. In this research report, Physician No. 184, which gave the researchers their ‘a-ha’ moment, is precisely the type of connector that we see in Figure 2. Now, we can find these connectors reliably in any social graphs via betweenness centrality.

Conclusion

As you can see, once you start looking at other graph metrics, or combination of metrics, you can glean an enormous amount of insight. If we marry these social graph metrics to the participation metrics and behavioral data that we track, you can really gain some deep intelligence about your community members. But I don’t want to write a whole book here, so I will stop for now.

For the past few weeks, I’ve been talking about nothing but social network analysis and showing you social graphs. I am going to take a break from social graphs for a while and talk about some new topics next time. Of course, if you have any comments or questions, or if there is a particular topic in social analytics that you would like me to cover, let me know.

This article was originally posted on the Lithosphere.

Guest Author: Dr. Michael Wu
Lithium Technologies Inc.

Michael Wu is the Principal Scientist of Analytics at Lithium Technologies Inc. Michael received his Ph.D. from UC Berkeley’s Biophysics graduate program. He is applying similar data-driven methodologies to investigate and understand the complex dynamics within online communities as well as the greater social web. You can follow Michael on Twitter at @Mich8elWu or on LinkedIn at Michael Wu PhD.